\newproblem{lay:1_2_8}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.2.8}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Find the general solution of the system whose augmented matrix is 
	\begin{center}
		$\begin{pmatrix} 1 & -3 & 0 & -5 \\ -3 & 7 & 0 & 9 \end{pmatrix}$
	\end{center}
}
{
   % Solution
	The augmented matrix is row equivalent to
	\begin{center}
		$\begin{pmatrix} 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & 3 \end{pmatrix}$
	\end{center}
	That represents the equations
	\begin{center}
		$x_1=4$ \\
		$x_2=3$
	\end{center}
	and there is no constraint for $x_3$. Therefore, the set of solutions of the equation system is
	\begin{center}
		$S=\{(4,3,x_3) \quad \forall x_3\in\mathbb{R}\}$
	\end{center}
}
\useproblem{lay:1_2_8}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
